An incomplete Hessian Newton minimization method and its application in a chemical database problem |
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Authors: | Dexuan Xie Qin Ni |
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Institution: | (3) Dip. Inform. e Sistemistica Univ. Roma ‘La Sapienza’, Roma, Italy |
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Abstract: | To efficiently solve a large scale unconstrained minimization problem with a dense Hessian matrix, this paper proposes to
use an incomplete Hessian matrix to define a new modified Newton method, called the incomplete Hessian Newton method (IHN).
A theoretical analysis shows that IHN is convergent globally, and has a linear rate of convergence with a properly selected
symmetric, positive definite incomplete Hessian matrix. It also shows that the Wolfe conditions hold in IHN with a line search
step length of one. As an important application, an effective IHN and a modified IHN, called the truncated-IHN method (T-IHN),
are constructed for solving a large scale chemical database optimal projection mapping problem. T-IHN is shown to work well
even with indefinite incomplete Hessian matrices. Numerical results confirm the theoretical results of IHN, and demonstrate
the promising potential of T-IHN as an efficient minimization algorithm. |
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Keywords: | |
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